论文标题
用葡萄藤构建多元分布函数：朝向多元亮度和质量功能
Constructing a multivariate distribution function with a vine copula: toward multivariate luminosity and mass functions
论文作者
论文摘要
在巨大的多波长调查的时代，对构建多维分布函数的方法的需求正在增加。我们提出了一种系统的方法来通过使用Copula来构建星系的双变量光度或质量功能。它允许我们在仅知道其边际分布时构建分布函数，并且我们必须从数据中估算依赖性结构。一个典型的例子是，我们在某些波长上具有单变量的光度函数以进行调查，但是关节分布尚不清楚。 Copula方法的主要限制是，除了某些特殊情况（例如多维高斯）外，将关节功能扩展到更高维度并不容易。即使我们在某些幸运的情况下发现了这种多元分析功能，它通常会僵化和不切实际。在这项工作中，我们展示了一种系统的方法，可以扩展副方法，以通过葡萄藤无限地更高维度。这是基于一般多元分布的成对孔隙分解。我们展示了葡萄藤的结构是如何柔性和扩展的。我们还提供了一个构建恒星质量 - 原子气体 - 分子气3维质量功能的例子。我们证明了该功能最佳功能形式的最大似然估计以及通过藤副群的正确选择。
The need for a method to construct multidimensional distribution function is increasing recently, in the era of huge multiwavelength surveys. We have proposed a systematic method to build a bivariate luminosity or mass function of galaxies by using a copula. It allows us to construct a distribution function when only its marginal distributions are known, and we have to estimate the dependence structure from data. A typical example is the situation that we have univariate luminosity functions at some wavelengths for a survey, but the joint distribution is unknown. Main limitation of the copula method is that it is not easy to extend a joint function to higher dimensions ($d > 2$), except some special cases like multidimensional Gaussian. Even if we find such a multivariate analytic function in some fortunate case, it would often be inflexible and impractical. In this work, we show a systematic method to extend the copula method to unlimitedly higher dimensions by a vine copula. This is based on the pair-copula decomposition of a general multivariate distribution. We show how the vine copula construction is flexible and extendable. We also present an example of the construction of an stellar mass--atomic gas--molecular gas 3-dimensional mass function. We demonstrate the maximum likelihood estimation of the best functional form for this function, as well as a proper model selection via vine copula.
